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Macaulay2Doc :: fine control of a Groebner basis computation

fine control of a Groebner basis computation

Sometimes a Groebner basis computation doesn't finish quickly enough. If so then this section might be of use. THIS PAGE IS UNDER CONSTRUCTION.

Partially computed Groebner bases

Suppose that you have computed part of a Groebner basis. For example, you may have interrupted the computation using CTRL-C (typing 'c' while holding the CTRL key down, in emacs, you have to type CTRL-C twice), or you may have given options requesting only partial computation.
i1 : R = ZZ/32003[a..e];
i2 : I = ideal(random(3,R),random(3,R),random(3,R))

                 3         2            2         3         2               
o2 = ideal (4946a  + 15130a b + 10667a*b  + 13156b  + 11207a c + 3599a*b*c +
     ------------------------------------------------------------------------
          2           2         2         3       2                     2   
     6440b c + 7758a*c  - 474b*c  - 14376c  - 840a d - 4011a*b*d - 7106b d +
     ------------------------------------------------------------------------
                                  2           2           2          2  
     909a*c*d - 4979b*c*d + 15104c d + 3525a*d  + 11153b*d  + 6551c*d  +
     ------------------------------------------------------------------------
          3        2                      2                            
     8468d  + 5073a e - 10045a*b*e + 6479b e - 10756a*c*e + 7041b*c*e -
     ------------------------------------------------------------------------
          2                                                2            2  
     2450c e + 14408a*d*e + 1525b*d*e - 10569c*d*e - 11993d e + 15231a*e  +
     ------------------------------------------------------------------------
            2          2          2        3          3         2   
     1601b*e  - 7985c*e  - 6424d*e  - 4029e , - 12593a  - 13073a b -
     ------------------------------------------------------------------------
             2        3        2                      2            2  
     10694a*b  + 2679b  + 2430a c + 11183a*b*c + 9817b c - 11848a*c  -
     ------------------------------------------------------------------------
             2        3       2                     2                
     11216b*c  - 9620c  - 945a d - 3984a*b*d - 6958b d + 13776a*c*d +
     ------------------------------------------------------------------------
                       2           2           2           2        3  
     15782b*c*d + 4955c d - 5195a*d  - 12435b*d  - 15426c*d  - 4191d  -
     ------------------------------------------------------------------------
          2                      2                                 2   
     2087a e - 12405a*b*e - 4288b e - 2469a*c*e - 4681b*c*e - 7072c e +
     ------------------------------------------------------------------------
                                               2           2          2  
     6201a*d*e + 3701b*d*e - 8496c*d*e - 14127d e + 7974a*e  - 8899b*e  -
     ------------------------------------------------------------------------
            2          2      3          3       2           2        3  
     9356c*e  - 2783d*e  - 68e , - 10405a  - 504a b + 6148a*b  - 2434b  -
     ------------------------------------------------------------------------
        2                    2           2           2         3        2   
     64a c + 829a*b*c + 2008b c + 2416a*c  + 11051b*c  + 13653c  - 2115a d +
     ------------------------------------------------------------------------
                       2                                  2            2  
     11817a*b*d - 5514b d + 15159a*c*d - 6354b*c*d - 6501c d - 12542a*d  +
     ------------------------------------------------------------------------
            2           2         3        2                      2   
     4660b*d  + 15279c*d  - 13242d  + 1271a e + 15465a*b*e + 8134b e +
     ------------------------------------------------------------------------
                                 2                                        
     8757a*c*e - 2959b*c*e + 408c e + 4853a*d*e + 8542b*d*e + 14027c*d*e -
     ------------------------------------------------------------------------
           2            2          2          2          2         3
     15505d e + 10444a*e  - 7456b*e  - 4878c*e  + 8476d*e  - 13202e )

o2 : Ideal of R
i3 : gens gb(I,PairLimit=>7);

             1       7
o3 : Matrix R  <--- R
Get the Groebner basis object:
i4 : g = gb(I,StopBeforeComputation => true);
i5 : leadTerm gens g

o5 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o5 : Matrix R  <--- R
We can make a Groebner basis snapshot by using StopBeforeComputation, or gbSnapshot:
i6 : gens gb(I,StopBeforeComputation => true)

o6 = | ab2+9362b3-11651a2c-12986abc-8035b2c-9632ac2+2657bc2-14491c3+3980a2d+
     ------------------------------------------------------------------------
     8773abd+7349b2d-11373acd+9105bcd-15132c2d+8882ad2-14493bd2-877cd2-8425d3
     ------------------------------------------------------------------------
     +7522a2e+8185abe+7661b2e-5667ace+6881bce+8442c2e-12834ade-375bde-6350cde
     ------------------------------------------------------------------------
     -573d2e+4666ae2-2533be2-7146ce2-14044de2+13044e3
     ------------------------------------------------------------------------
     a2b-2563b3+460a2c-2251abc-453b2c-2777ac2-3104bc2+6030c3+5242a2d+3036abd-
     ------------------------------------------------------------------------
     1706b2d+14493acd-4840bcd+7338c2d-4025ad2-13902bd2-2003cd2+11476d3+
     ------------------------------------------------------------------------
     7459a2e+1311abe-3254b2e-5296ace-2579bce-2437c2e-2558ade-8895bde-5392cde-
     ------------------------------------------------------------------------
     13404d2e-10652ae2+5776be2-6936ce2+5927de2-9871e3
     ------------------------------------------------------------------------
     a3-4014b3-6805a2c+14492abc+1524b2c+8616ac2+329bc2-299c3-9556a2d-3595abd+
     ------------------------------------------------------------------------
     9808b2d+10139acd+8989bcd-2763c2d+15099ad2-4701bd2-6448cd2-11272d3+
     ------------------------------------------------------------------------
     5135a2e+9471abe+14695b2e+10219ace+15076bce-11063c2e-1336ade+8556bde-
     ------------------------------------------------------------------------
     1007cde-792d2e-13134ae2+8448be2+15605ce2-15162de2-5488e3
     ------------------------------------------------------------------------
     b3c-12415a2c2+15824abc2+5042b2c2-4186ac3-11802bc3-1918c4-5811b3d+
     ------------------------------------------------------------------------
     4724a2cd-3061abcd-15271b2cd+13309ac2d-6262bc2d+14727c3d-11996a2d2-
     ------------------------------------------------------------------------
     6651abd2-15251b2d2+978acd2+15069bcd2+6255c2d2+13106ad3+7534bd3+5932cd3+
     ------------------------------------------------------------------------
     11661d4-12945b3e+9035a2ce+7343abce+9333b2ce-11655ac2e-11846bc2e-10753c3e
     ------------------------------------------------------------------------
     +14338a2de-2386abde+8897b2de+12884acde+15234bcde-11184c2de+15003ad2e+
     ------------------------------------------------------------------------
     1096bd2e-5919cd2e-607d3e-15048a2e2+10659abe2+15045b2e2+3633ace2-3155bce2
     ------------------------------------------------------------------------
     -8263c2e2-4961ade2+10814bde2+5663cde2+14517d2e2+13751ae3-2515be3-
     ------------------------------------------------------------------------
     15241ce3+6320de3-6050e4
     ------------------------------------------------------------------------
     b4+14441a2c2+4805abc2-522b2c2-764ac3+7405bc3-9205c4+2286b3d+14189a2cd-
     ------------------------------------------------------------------------
     12919abcd-2229b2cd-11619ac2d-6189bc2d+9878c3d-5706a2d2-12590abd2-
     ------------------------------------------------------------------------
     4813b2d2+4913acd2-9229bcd2+13468c2d2-11373ad3+1774bd3-1985cd3+4603d4+
     ------------------------------------------------------------------------
     12296b3e-9222a2ce+12013abce+4731b2ce-2917ac2e+9555bc2e+18c3e-13418a2de-
     ------------------------------------------------------------------------
     4724abde-14299b2de-8450acde-14447bcde-6070c2de+13571ad2e+14560bd2e-
     ------------------------------------------------------------------------
     5759cd2e-13300d3e-14530a2e2+8469abe2-6503b2e2-6210ace2+11262bce2+
     ------------------------------------------------------------------------
     7918c2e2+2226ade2-3012bde2+8837cde2-8021d2e2-7669ae3+537be3+8641ce3-
     ------------------------------------------------------------------------
     6840de3+1190e4 abc3+10050b2c3-8435ac4-8845bc4+8700c5-3957a2c2d+
     ------------------------------------------------------------------------
     15455abc2d-12100b2c2d-6963ac3d+4938bc3d+4587c4d+15436b3d2-5226a2cd2+
     ------------------------------------------------------------------------
     5900abcd2-6562b2cd2+13281ac2d2-15233bc2d2-12263c3d2-412a2d3-14267abd3-
     ------------------------------------------------------------------------
     14229b2d3-5790acd3+9207bcd3+11514c2d3-2145ad4+1085bd4+9331cd4+1815d5+
     ------------------------------------------------------------------------
     379a2c2e+12625abc2e+12988b2c2e+14604ac3e+7694bc3e-13914c4e+8830b3de-
     ------------------------------------------------------------------------
     11284a2cde+222abcde+5230b2cde-14992ac2de-5018bc2de-8282c3de-15436a2d2e+
     ------------------------------------------------------------------------
     4368abd2e+9483b2d2e-9458acd2e-8184bcd2e+12727c2d2e+15810ad3e-5464bd3e+
     ------------------------------------------------------------------------
     8382cd3e-10513d4e-14165b3e2-10890a2ce2-9142abce2+13098b2ce2-8025ac2e2-
     ------------------------------------------------------------------------
     5575bc2e2+3450c3e2-12152a2de2-13439abde2+8957b2de2-7356acde2-2179bcde2+
     ------------------------------------------------------------------------
     15116c2de2+6821ad2e2+6394bd2e2-8250cd2e2-12550d3e2+11468a2e3-9192abe3-
     ------------------------------------------------------------------------
     10316b2e3+15213ace3-2897bce3-11288c2e3+10541ade3+10166bde3-4911cde3-
     ------------------------------------------------------------------------
     8711d2e3+4882ae4+14785be4-9069ce4+10780de4+13379e5
     ------------------------------------------------------------------------
     a2c3-3004b2c3-5292ac4+8766bc4+8355c5-1003a2c2d-5081abc2d+3101b2c2d-
     ------------------------------------------------------------------------
     3252ac3d+2206bc3d+5728c4d-669b3d2-11491a2cd2-2727abcd2-13545b2cd2+
     ------------------------------------------------------------------------
     13722ac2d2+5214bc2d2-15684c3d2-4760a2d3-2934abd3-2149b2d3+12838acd3-
     ------------------------------------------------------------------------
     99bcd3+3478c2d3+4299ad4+4517bd4+15723cd4-6153d5+11654a2c2e+13996abc2e-
     ------------------------------------------------------------------------
     6646b2c2e-14008ac3e-335bc3e-15085c4e-12548b3de-12623a2cde+6628abcde-
     ------------------------------------------------------------------------
     1250b2cde+8472ac2de+13608bc2de-9664c3de+15886a2d2e-10579abd2e-11510b2d2e
     ------------------------------------------------------------------------
     -4513acd2e+348bcd2e-6317c2d2e-10640ad3e-12712bd3e-11226cd3e+6078d4e+
     ------------------------------------------------------------------------
     11468b3e2-5317a2ce2-9064abce2+11680b2ce2+7999ac2e2-14611bc2e2-9399c3e2-
     ------------------------------------------------------------------------
     10594a2de2-6657abde2-903b2de2+5272acde2-10636bcde2-729c2de2-10720ad2e2+
     ------------------------------------------------------------------------
     2862bd2e2+4619cd2e2-12828d3e2-12636a2e3+7405abe3-10203b2e3-1952ace3-
     ------------------------------------------------------------------------
     8400bce3+7477c2e3-6723ade3+15022bde3-12755cde3-4841d2e3+5497ae4+11418be4
     ------------------------------------------------------------------------
     -14160ce4-8772de4+1740e5 |

             1       7
o6 : Matrix R  <--- R
i7 : leadTerm gbSnapshot(I)

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R